Question

A passenger railroad car has a total of 8 wheels. Springs on each wheel compress--slightly--when the car is loaded. Ratings for the car give stiffness per wheel (the spring constant, treating the entire spring assembly as a single spring) as 2.8×10⁷N/m.
When 30 passengers, each with average mass of 80 kg, board the car, how much does the car move down on its spring suspension? Assume that each wheel supports 1/8 the weight of the car.

Answer 1

Answer:

0.0001501 m

Explanation:

g = Acceleration due to gravity = 9.81 m/s²

k = Spring constant = $2.8\times 10^7\ N/m$

x = Compression of spring

F = Force = Mg

Mass of passengers

$M=30\times 80=2400\ kg$

Each spring supports the following mass

$m=\frac{2400}{8}=300\ kg$

Force of spring

$F=kx\\\Rightarrow x=\frac{F}{k}\\\Rightarrow x=\frac{mg}{k}\\\Rightarrow x=\frac{300\times 9.81}{2.8\times 10^7}\\\Rightarrow x=0.0001051\ m$

The car moves down by 0.0001501 m